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QuestionSolve the equations: (b) 8x+5=3(2x−11)8x + 5 = 3(2x - 11) and (e) 1−4x8=3x−74\frac{1 - 4x}{8} = \frac{3x - 7}{4}.

Studdy Solution

STEP 1

Assumptions1. The equations provided are linear equations. . The variable 'x' represents the same value in both sides of the equations.
3. The goal is to solve for the variable 'x'.
Problem (b): 8x+5=3(x−11)8x+5=3(x-11)

STEP 2

First, we need to distribute the on the right side of the equation.
8x+5=∗2x−∗118x+5=*2x-*11

STEP 3

Calculate the multiplication on the right side of the equation.
8x+5=6x−338x+5=6x-33

STEP 4

Rearrange the equation to bring like terms together. Subtract 6x6x from both sides of the equation.
8x−6x=6x−6x−33−8x-6x=6x-6x-33-

STEP 5

implify the equation.
2x=−382x=-38

STEP 6

Finally, to solve for 'x', divide both sides of the equation by2.
x=−382x=\frac{-38}{2}

STEP 7

Calculate the value of 'x'.
x=−19x=-19Problem (e): 1−4x=3x−74\frac{1-4x}{}=\frac{3x-7}{4}

STEP 8

To simplify the equation, we can cross-multiply.
(1−4x)∗4=(3x−7)∗8(1-4x)*4=(3x-7)*8

STEP 9

Calculate the multiplication on both sides of the equation.
4−16x=24x−564-16x=24x-56

STEP 10

Rearrange the equation to bring like terms together. Add 16x16x to both sides of the equation.
4=24x+16x−564=24x+16x-56

STEP 11

implify the equation.
4=40x−564=40x-56

STEP 12

Add 5656 to both sides of the equation.
4+56=40x+56−564+56=40x+56-56

STEP 13

implify the equation.
60=40x60=40x

STEP 14

Finally, to solve for 'x', divide both sides of the equation by40.
x=6040x=\frac{60}{40}

STEP 15

Calculate the value of 'x'.
x=.5x=.5So, the solution to the equations are x=−19x=-19 for problem (b) and x=.5x=.5 for problem (e).

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